Find the work done by the force F = 2 ( y 2 i ^ + 2 x 2 j ^ ) , x \& y are in meters around the path shown. If the work done is ad b then find the value of a + b .

W = ∫ F ⋅ d x = 2 ∫ ( y 2 d x + 2 x 2 d y ) around the square loop. W O A = 0 , W A B = 2 [ 0 + 2 d 2 ⋅ d ] = 4 d 3 W BC = 2 [ d 2 ( − d ) + 0 ] = − 2 d 3 , W C D = 0 W = 0 + 4 d 3 − 2 d 3 + 0 = 2 d 3 , so a = 2, b = 3 and a + b = 5.

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PhysicsW.E.P.Calculation of workMedium2 minQB

PhysicsMediuminteger

Find the work done by the force $F = 2 (y^{2} \hat{i} + 2 x^{2} \hat{j})$ , x \& y are in meters around the path shown. If the work done is $ad^{b}$ then find the value of $a + b$ .

Answer:

Solution:

$W = \int F \cdot d x = 2 \int (y^{2} d x + 2 x^{2} d y)$ around the square loop.

$W_{O A} = 0, W_{A B} = 2 [0 + 2 d^{2} \cdot d] = 4 d^{3}$

$W_{BC} = 2 [d^{2} (- d) + 0] = - 2 d^{3}, W_{C D} = 0$

$W = 0 + 4 d^{3} - 2 d^{3} + 0 = 2 d^{3}$ , so a = 2, b = 3 and a + b = 5.

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Calculation of work

⏱ 2mℹ️ Source: QB

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